courseware

Path-Based Scheduling

Sune Fallgaard Nielsen

Informatics and Mathematical ModellingTechnical University of Denmark

Richard Petersens Plads, Building 322DK2800 Lyngby, Denmark

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Overview

Motivation Introduction – Prior work / new paradigm Defining problem and model constraints Solution:

AFAP Scheduling Algorithm The scheduling steps using AFAP

Results Conclussion

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Motivation

Derive a synthesis tool which:

Minimizes the number of control steps

Takes constraints into account

Considers loops and conditional branches

( which no prior work has done )

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Introduction

Prior work: scheduling <- minimize cost function

Cost function:

- Fixed hardware (uP): Number of states

- Hardware syntheses: Number of states + hardware Scheduling:

Minimizing the cost function by moving operations around Optimal solution:

- Optimal schedule emphasizing concurrency

- Force directed serialization + moving mobile operations

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Introduction / Problem

Path-Based Scheduling for Synthesis:

Forget cost functions!

Instead: Emphasize on conditional branches, loops

Minimize number of control steps

- taking constraints into account ( main problem )

Main problem: Gain advantages from looking at branches

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Constraints

Internal constraints:- Units can only receive and output values once per cycle- With single phase clock this implies single use per cycle

External constraints:- Amount of hardware available:- Area, units etc.- Timing constraints

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AFAP scheduling

AFAP ( As Fast As Possible )

Basic idea: Control-flow directed graph

- Nodes (ops.). Edges (precedence relations).

Longest path: Max number of operations. Cycles only traversed once (%loop unfolding)

Scheduling: Put as many operations into one control step as possible in all possible paths.

Goal: Finite State Machine to implement control

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AFAP Scheduling for a single path

AFAP Sch. for a single path ( no loops/branches )

1. Longest path is computed

2. For every path constraints are computed (variables, IOs, func. Units, max delay) and “Cut”s are lain in according to constraints

3. Interval graph is formed with cliques (complete subgraph of all poss. edges)

4. Cuts an cliques are stored for later processing

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AFAP Scheduling for a single path

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AFAP – The algorithm

The four steps to Nirvana ( or something ):

1. Transform the control flow graph into a directed acyclic graph (DAG)

2. All paths in the DAG are scheduled AFAP

3. Schedules are overlapped in a way to minimize the number of control steps

4. The finite state machine is built.

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AFAP – Example

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Building finite state machine

Trivial finite state machine design:

Overlapping of intervals to form states (same cut -> same state)

Construct state transitions (figure out control signals for each state)

Construct state transition conditions (rules for looping, waiting etc)

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Results

Comparison is difficult since goals are different. Different compiler machines used

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Conclusion: Good things / bad things

Good things:Real life examplesGood results

Bad things:No support for secondary hardware constraints - like busses, registers, ports etc.No smart loop unfolding capabilitiesNo pipeline scheduling capabilitiesNo instruction execution reordering supported